Transcript Writing a Ratio as a Fraction

Chapter 5
Percent
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5.1
Ratio and Proportion
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Writing Ratios as Fractions
A ratio is a quotient of two quantities.
1 to 2 or 1
or 1 : 2
2
Writing a Ratio as a Fraction
The order of the quantities is important when writing
ratios. To write a ratio as a fraction, write the first
number of the ratio as the numerator of the fraction
and the second number as the denominator.
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Example
Write the ratio 15 to 23 using fractional notation.
15
23
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Writing Ratios in Simplest Form
Write the ratio of $25 to $15 as a fraction in simplest
form.
$25 25 5  5 5



$15 15 3  5 3
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Writing Ratios in Simplest Form
Write the ratio of 2.6 to 3.1 as a fraction in simplest
form.
2.6 2.6

1
3.1 3.1
2.6 10 2.6 10 26

 

3.1 10 3.1 10 31
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Writing Ratios in Simplest Form
Write the ratio of 1 1 to 2 7 as a fraction in simplest
5
10
form.
1
1
5  11  2 7
7
5
10
2
10
6 27 6 10
 
 
5 10 5 27
6 10 2  3  2  5 4



5  27 5  3  3  3 9
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Writing Ratios in Simplest Form
Given the rectangle shown:
a. Find the ratio of its width to its length.
b. Find the ratio of its length to its perimeter. 7 feet
a. width  5 feet  5
length
7 feet
7
5 feet
b. Perimeter = 7 + 5 + 7 + 5 = 24 feet
length
7 feet
7


perimeter 24 feet 24
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Writing Rates as Fractions
A special type of ratio is a rate. A rate is used to
compare different kinds of quantities.
3 miles
1 mile

33 minutes 11 minutes
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Example
Write the rate as a fraction in simplest form.
10 nails every 6 feet
10 nails 5 nails

6 feet
3 feet
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Example
Write each rate as a fraction in simplest form.
a. $2160 for 12 weeks
2160 dollars 180 dollars

12 weeks
1 week
b. 360 miles on 16 gallons of gasoline
360 miles 45 miles

16 gallons 2 gallons
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Writing Proportions
A proportion is a statement that two ratios or rates are
equal. For example,
5 10

6 12
is a proportion. We can read this as “5 is to 6 as 10 is
to 12.”
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Example
Write the statement 12 diamonds is to 15 rubies as 4
diamonds is to 5 rubies as a proportion.
diamonds  12 4  diamonds

rubies  15 5  rubies
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Determining Whether Proportions are True
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Example
Is 4.1  2.9 a true proportion?
7
5
Determine the cross products.
4.1 2.9

7
5
4.1 5  7  2.9
20.5  20.3
Since the cross products are not equal. The proportion is
false.
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Finding Unknown Numbers in Proportions
When one number of a proportion is unknown, we can
use cross products to find the unknown numbers.
Finding an Unknown Value n in a Proportion
Step 1: Set the cross products equal to each other.
Step 2: Divide the number not multiplied by n by the
number multiplied by n.
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Example
Find the value of the unknown number n.
51 3

34 n
51  n  34  3
51n  102
Set cross products equal.
Multiply.
102
n
51
n2
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Solving Problems by Writing Proportions
On a chamber of commerce map of Abita Springs, 5
miles corresponds to 2 inches. How many miles
correspond to 7 inches?
miles
miles

inches inches
5 n

2 7
57  2 n
35  2n
35
n
2
1
17  n
2
7 inches corresponds to 17.5 miles
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Solving Problems by Writing Proportions
The standard does of an antibiotic is 3 cc for every 50pounds of body weight. At this rate, find the standard
dose for a 130-lb woman.
cc
cc

pounds pounds
3
n

50 130
3 130  50  n
390  50n
390
n
50
7.8  n
The standard dose for a 130-lb woman is 7.8 cc.
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